Question

A boy rides on a pony that is walking with constant velocity. The boy leans over to one side, and a scoop of ice cream falls from his ice cream cone. Describe the path of the scoop of ice cream as seen by (a) the child and (b) his parents standing on the ground nearby.

Short answer

(a) The boy sees the scoop fall straight down; (b) the parents see a parabolic trajectory.

Step-by-step solution

Analyze the Situation from the Boy's Viewpoint

From the boy's perspective, he is moving with the pony at a constant velocity. Therefore, relative to him, he is at rest. When the ice cream scoop falls, it appears to simply drop vertically downwards. This is because relative to himself and the pony, there is no horizontal motion of the ice cream scoop.

Analyze the Situation from the Parents' Viewpoint

From the viewpoint of the parents who are standing stationary on the ground, the boy and the pony are moving forward with a constant velocity. When the scoop of ice cream falls, it retains the horizontal velocity component that's the same as that of the pony. Thus, to the parents, the path of the ice cream scoop seems to follow a parabolic trajectory because it moves horizontally while simultaneously falling under the influence of gravity.

Key concepts

Relative Velocity

Relative velocity is a way of understanding the motion of an object in relation to another moving object. Imagine you are sitting in a car on a highway. To you, a car moving at the same speed in the next lane seems to be at rest relative to you. This is because both you and the other car share the same velocity relative to the road.
In the example of the boy and the falling ice cream, from the boy's point of view, the scoop seems to fall straight down. This is because he's moving with the pony, and thus perceives the ice cream as having zero horizontal velocity. From the parents' perspective on the ground, the ice cream also holds the forward velocity of the pony even as it drops, hence it seems to travel in a curve. This illustrates how motion can seem different depending on the observer's relative motion.

Frame of Reference

A frame of reference is like a lens through which you observe motion. It is crucial because it defines how motion is described and perceived. Think about standing still on the ground watching cars pass by. Your frame of reference is the Earth.
### Example
For the boy on the pony, his frame of reference is moving with the pony. In his frame, he and the pony are effectively at rest. Therefore, the ice cream simply falls vertically downward without any horizontal motion. However, for the parents standing on the ground, their frame of reference is fixed. As they watch, the ice cream not only falls down due to gravity but also travels forward. This combination makes the ice cream’s path appear like an arc or a parabola. This difference shows the importance of choosing a frame of reference to accurately describe motion.

Constant Velocity

Constant velocity means that an object's speed and direction do not change. If a pony is walking forward at a constant velocity, it moves in a straight line without speeding up, slowing down, or changing direction. This consistency allows for easy calculations of movement as there's no acceleration to consider.

• **Speed:** Rate at which an object covers distance (like 5 meters per second).
• **Direction:** The line or path along which something moves, points, or faces.

In our scenario, the pony moves with constant velocity, so its horizontal speed remains steady. From the parents' viewpoint, any object that separates from the pony, like the ice cream scoop, initially continues with this same constant velocity. However, gravity then introduces a downward acceleration, creating that parabolic path observed. Therefore, a constant velocity simply means keeping a steady course unless acted upon by other forces.